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MNRAS 000, 1–13 (20XX) Preprint 10 November 2015 Compiled using MNRAS LATEX style file v3.0

Doppler-imaging of the planetary debris disc at the white

dwarf SDSSJ122859.93+104032.9

Christopher J. Manser 1⋆, Boris T. Gansicke 1, Thomas R. Marsh 1,

Dimitri Veras 1, Detlev Koester 2, Elme Breedt 1, Anna F. Pala 1,

Steven G. Parsons 3, John Southworth 41 Department of Physics, University of Warwick, Coventry CV4 7AL, UK2 Institut fur Theoretische Physik und Astrophysik, University of Kiel, 24098 Kiel, Germany3 Departamento de Fısica y Astronomıa, Universidad de Valparaıso, Avenida Gran Bretana 1111, Valparaıso, Chile4 Astrophysics Group, Keele University, Staffordshire, ST5 5BG, UK

Accepted 20XX. Received 20XX; in original form 20XX

ABSTRACT

Debris discs which orbit white dwarfs are signatures of remnant planetary sys-tems. We present twelve years of optical spectroscopy of the metal-polluted whitedwarf SDSS J1228+1040, which shows a steady variation in the morphology of the8600 A Ca ii triplet line profiles from the gaseous component of its debris disc. Weidentify additional emission lines of O i, Mg i, Mg ii, Fe ii and Ca ii in the deep co-added spectra. These emission features (including CaH&K) exhibit a wide range instrength and morphology with respect to each other and to the Ca ii triplet, indicatingdifferent intensity distributions of these ionic species within the disc. Using Dopplertomography we show that the evolution of the Ca ii triplet profile can be interpretedas the precession of a fixed emission pattern with a period in the range 24–30years.The Ca ii line profiles vary on time-scales that are broadly consistent with generalrelativistic precession of the debris disc.

Key words: Stars: individual: SDSS J122859.93+104032.9 – white dwarfs – Circum-stellar matter – accretion, accretion discs – line: profiles.

1 INTRODUCTION

The first discovery of a debris disc around a white dwarf wasmade by Zuckerman & Becklin (1987) via the detection ofan infrared excess at G29–38, which was later interpretedas the emission from circumstellar dust by Graham et al.(1990). This disc is thought to be the result of the tidaldisruption of an asteroid or comet within a remnant plan-etary system that survived the main sequence evolution ofthe white dwarf progenitor (Jura 2003; Debes et al. 2012;Veras et al. 2014). Since the discovery of infrared emissionfrom G29–38, debris discs have been detected at more thanthirty additional white dwarfs (Kilic et al. 2006; Farihi et al.2008, 2009; Jura et al. 2009; Debes et al. 2011; Hoard et al.2013; Bergfors et al. 2014; Rocchetto et al. 2015), which arein all (but possibly one, see Xu et al. 2015) cases accompa-nied by the detection of trace metals in the white dwarfphotosphere (Koester et al. 1997; Zuckerman et al. 2007;Jura & Young 2014).

⋆ E-mail: C.Manser@warwick.ac.uk

Two decades after the discovery of dust at G29–38, Gansicke et al. (2006) identified a gaseous disc aroundthe white dwarf SDSSJ122859.93+104032.9 (henceforthSDSSJ1228+1040) via the detection of double peaked emis-sion lines of Ca ii at 8498.02 A, 8542.09 A, 8662.14 A, (hence-forth the Ca ii triplet), which is indicative of Keplerian rota-tion in a flat disc (Horne & Marsh 1986). Spitzer and HST

follow-up observations detected circumstellar dust and aplethora of metallic absorption lines, respectively; strength-ening the connection of the gaseous material to the pres-ence of a remnant planetary system around this white dwarf(Brinkworth et al. 2009; Gansicke et al. 2012). The mor-phology of these emission lines provided firm dynamical con-firmation that the debris disc resides within the tidal disrup-tion radius of the white dwarf.

Despite intense searches over the last decade,gaseous discs have been found around only seven whitedwarfs (Gansicke et al. 2006, 2007, 2008; Gansicke 2011;Farihi et al. 2012; Melis et al. 2012; Wilson et al. 2014).All seven also exhibit infrared excess from dusty discs,five of which were discovered after their gaseous counter-

c© 20XX The Authors

2 Christopher J. Manser et al.

part (Dufour et al. 2010; Brinkworth et al. 2012). Only inHE1349–2305 and SDSSJ095904.69–020047.6 (henceforthSDSSJ0959–0200) were the Ca ii emission lines detected af-ter the initial discovery of a dusty disc. Only a small frac-tion of the systems hosting a dust-dominated debris discalso have an observable gaseous component, implying thatthe presence of detectable amounts of gas is not inherent tothe presence of a debris disc.

The origin of these seven gaseous discs is still unclear.Several scenarios have been proposed, including runawayfeedback between sublimation and the ensuing gas drag onthe dust, leading to a rapid increase in the accretion rateonto the white dwarf (Rafikov 2011; Metzger et al. 2012),and secondary impacts of asteroids on an existing debrisdisc (Jura 2008). Both cases involve dynamic interactions inthe disc which might lead to detectable levels of variability.

Changes in the strength and morphology of theCa ii triplet have been reported in a number ofsystems. SDSSJ161717.04+162022.4 (Wilson et al. 2014,henceforth SDSSJ1617+1620) was identified to host atransient gaseous disc, which following its first de-tection monotonically decreased in strength over eightyears until it dropped below detectability. In con-trast SDSSJ084539.17+225728.0 (Gansicke et al. 2008;Wilson et al. 2015, henceforth SDSSJ0845+2257) showschanges in the morphology of the Ca ii triplet, but not inthe strength of the lines. We also note that SDSSJ0959–0200 has shown a large decrease in the infrared emissionfrom the dusty component of the debris disc, however notime-resolved observations of the gaseous disc have beenpublished (Farihi et al. 2012; Xu & Jura 2014).

We have been spectroscopically monitoring the whitedwarf SDSSJ1228+1040 for twelve years and report in thispaper pronounced changes in the morphology of the Ca iitriplet. We also show the first intensity map in velocity spaceof the Ca ii gas at SDSSJ1228+1040 using Doppler tomog-raphy.

2 OBSERVATIONS

2.1 The data

We obtained optical spectroscopy of SDSSJ1228+1040from 2003 to 2015 with several instruments: X-shooter(Vernet et al. 2011) and the Ultraviolet and Visual EchelleSpectrograph (UVES, Dekker et al. 2000) which are bothon the ESO Very Large Telescope (VLT); the 2.5m SloanDigital Sky Survey telescope (SDSS, data retrieved fromDR7 and DR9, Gunn et al. 2006; Abazajian et al. 2009;Eisenstein et al. 2011; Ahn et al. 2014; Smee et al. 2013);and the Intermediate dispersion Spectrograph and ImagingSystem (ISIS) on the William Herschel Telescope (WHT).These observations are summarised in Table 1. The X-shooter and UVES data were reduced using the REFLEX

1

reduction work flow using the standard settings and op-timising the slit integration limits (Freudling et al. 2013).The sky spectrum of each observation was used to deter-mine the spectral resolution. We also report the parameters

1 Documentation and software for REFLEX can be obtained fromhttp://www.eso.org/sci/software/reflex/

of SDSSJ1228+1040 in Table 2. The first ISIS spectrum ofSDSSJ1228+1040 obtained on the WHT were reported inGansicke et al. (2006, 2007), the 2010 ISIS spectrum wasobtained with a similar setup, and was reduced in the samefashion (see Farihi et al. 2012 and Wilson et al. 2014 for ad-ditional details).

2.2 Telluric corrections

The X-shooter observations (as with all ground-based spec-troscopy) are affected by telluric lines, in particular aroundthe Ca ii triplet. We removed this contamination using152 empirical telluric templates from the X-shooter library(XSL), provided by Chen et al. (2014). Each template in-cludes the normalised telluric absorption features over thewavelength range 5300 – 10200 A. The telluric absorptiondoes not affect this entire range and hence we split thetemplates into seven smaller regions which we correct forindependently. We first continuum normalise the observedspectrum and then we fit each of the seven regions toall 152 templates with two free parameters; a wavelengthshift (for telescope flexure) and the intensity of the tel-luric features (which varies with the atmospheric conditionsbetween different observations). The best-fitting templatefor each region is used to correct that part of spectrum.An example of a telluric corrected X-shooter spectrum forSDSSJ1228+1040 is shown in Figure 1.

2.3 Velocity corrections

The observations of the Ca ii triplet were converted fromwavelength to velocity space using the rest wavelengths,8498.02 A, 8542.09 A, 8662.14 A, which are corrected for thesystemic velocity, i.e. the velocity along the line of sight.Gansicke et al. (2012) calculated a velocity difference of+57 ± 1 kms−1 between the photospheric absorption linesof the white dwarf and the interstellar ultraviolet absorptionlines in SDSSJ1228+1040. This value combines the systemicvelocity as well as the gravitational red-shift of the photo-spheric absorption lines at the white dwarf surface (Koester1987). Adopting a white dwarf mass and radius of 0.705M⊙

and 0.01169 R⊙, respectively (Koester et al. 2014), we ob-tain a gravitational red-shift of +38 ± 4 kms−1, resultingin a systemic velocity of +19 ± 4 km s−1. This velocity isused to shift the Ca ii triplet observations to the rest frameof the system as well as for Doppler Tomography discussedin Section 5. All the Ca ii triplet observations are shown invelocity space in Figure 2 and we discuss the evolution ofthe Ca ii triplet in the next section.

3 EVOLUTION OF THE CA II TRIPLET

STRUCTURE

3.1 Double peaked emission from a disc

Horne & Marsh (1986) showed that a circular gaseousdisc with a radially symmetric intensity distribution orbit-ing a central mass will produce symmetric double-peakedemission line profiles in velocity space (See Figure 1 ofHorne & Marsh 1986), due to the range in velocities acrossthe disc projected along the line of sight. Two properties

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Figure 1.X-shooter spectra (grey) of SDSSJ 1228+1040 (obtained in January 2011) together with a model fit (blue) using the atmosphericparameters (Table 2). The strongest emission and absorption lines have been labelled.

Table 1. Log of observations of SDSS J1228+1040. a Different exposure times for the individual UVES arms (blue / red lower andupper) and X-shooter arms (UVB / VIS). b Observations did not cover the Ca ii triplet. We did not use data collected by the NIR armof X-shooter as the signal-to-noise ratio was too poor.

Date Telescope/Instrument Wavelength Range [A] Resolution [A] Total Exposure Time [s] a

2003 March 27 SDSS 3800 – 9200 2.7 29002006 June 30 - July 01 WHT/ISIS 7500 – 9200 2.0 12000

2007 April 07 VLT/UVES 3045 – 9463 0.19 11800 / 113602007 June 06 VLT/UVES 3758 – 9463 0.18 5900 / 5680

2007 July 09 - 10 VLT/UVES 3757 – 9463 0.18 5900 / 56802008 January 10 VLT/UVES 3759 – 9464 0.18 5900 / 56802008 April 11 b VLT/UVES 3284 – 6649 0.13 11800 / 113602008 June 27 VLT/UVES 3758 – 9463 0.18 5900 / 56802008 July 19 VLT/UVES 3758 – 9463 0.18 5900 / 5680

2009 January 12 b VLT/UVES 3284 – 6650 0.14 5900 / 56802009 February 03 VLT/UVES 3758 – 9464 0.18 5900 / 5680

2009 April 04 VLT/UVES 3282 – 9463 0.18 17700 / 170402010 April 27 WHT/ISIS 8100 – 8850 1.1 1800

2011 January 22 VLT/X-Shooter 2990 – 10400 1.09 2840 / 14002011 May 29 VLT/X-Shooter 2990 – 10400 1.14 2840 / 14002011 June 14 VLT/X-Shooter 2990 – 10400 1.09 2840 / 1400

2012 March 26 VLT/X-Shooter 2990 – 10400 1.11 2840 / 14002014 March 06 VLT/X-Shooter 2990 – 10400 1.10 1971 / 30452014 June 02 VLT/X-Shooter 2990 – 10400 1.09 1314 / 20302015 May 11 VLT/X-Shooter 2990 – 10400 1.10 2380 / 25102015 May 18 VLT/UVES 3732 – 9463 0.20 2980 / 2960

Table 2. Atmospheric parameters for SDSS J1228+1040 (from Koester et al. 2014).

Teff [K] log g MWD [M⊙] RWD [R⊙]

20713 (281) 8.150 (0.089) 0.705 (0.051) 0.01169 (0.00078)

of the physical structure of the disc, the inner and outerradii, can be easily inferred from these profiles as the Kep-lerian velocity increases with decreasing distance from thecentral object. The inner radius of the disc is determinedfrom the maximum velocity, i.e. the point at which theemission drops to the continuum level; also known as theFull Width Zero Intensity (FWZI). We define the maximumred/blue-shifted velocities to represent the red/blue inneredges of the disc. The outer radius can be estimated fromthe peak separation in the double peaked profile. These ob-servationally derived radii, Robs, relate to the true radii, R,

via Robs = R sin2 i, where i is the inclination of the disc.This method was used by Gansicke et al. (2006) to derivethe observed inner and outer radii of SDSSJ1228+1040 tobe ≃ 0.64R⊙ and ≃ 1.2 R⊙, respectively.

A departure from the symmetric double-peaked profilecan reveal information about the physical structure of thedisc, as demonstrated by Steeghs & Stehle (1999) for theoccurence of spiral shocks in the disc (Steeghs et al. 1997;Steeghs 1999). An eccentric disc would generate an asym-metric double-peaked profile if viewed along the semi-minoraxis, as there is an asymmetry in the amount of material

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4 Christopher J. Manser et al.

emitting red and blue-shifted light. We use this insight be-low to discuss the changes in the emission profiles seen inSDSSJ1228+1040.

3.2 Variation of the calcium triplet profiles

The Ca ii triplet in SDSSJ1228+1040 has undergone an as-tonishing morphological evolution in the twelve years of ob-servations (Figure 2). The three individual line profiles varyin the same manner and we therefore use the term ”profile”to decribe their evolution. The initial spectra from 2003 and2006 show a double-peaked profile indicative of a circum-stellar disc with a red-dominated asymmetry. These obser-vations were interpreted as emission from an eccentric discwith a non isotropic intensity distribution (Gansicke et al.2006). The maximum velocities (highest blue or red-shift)in the disc measured from the 2006 observations were foundto be ± 560 ± 10 kms−1.

As the profiles evolve, there is a general smooth progres-sion from a red-dominated asymmetry to a blue-dominatedone. Throughout this evolution the morphology of the peaksalso changes, with the blue-shifted peak becoming strongerand sharper. In contrast, the red-shifted peak becomes shal-lower and weaker and extends to higher velocities, whichcan be seen first in the April 2009 observations. This ex-tension into the red is clearest in the January 2011 spec-trum with a maximum extension of +780 ± 10 kms−1. Theclear, sharp cut-off of the red wing of the profile is a suddenchange compared to the more gradual evolution in shapeand implies that the red-shifted inner edge of the disc hasmoved inwards to smaller radii (i.e. higher velocities). From2011–2015 the red wing decreases in extent, reducing themaximum velocity to +670 ± 10 km s−1, accompanied byan increase in strength, showing a clear reappearance of thered peak. Overall, the profile shifts to longer wavelengths,with the blue edge moving from −560 ± 10 kms−1 in July2006 to −390 ± 10 kms−1 in May 2015. The variation inthe red and blue velocities imply an asymmetry in the in-ner disc edge, as a circular Keplerian orbit would produceidentical red/blue velocities. In summary, the observed vari-ations clearly show that the inner edge of the gaseous discis not circular.

4 ADDITIONAL EMISSION LINES IN

SDSSJ1228+1040

In addition to the Ca ii triplet, Gansicke et al. (2006) re-ported emission of Fe ii 5169 / 5197 A, however these lineswere too weak to resolve the shape of their profiles. Byinspecting the averaged X-shooter UVB and VIS spectralarms, we clearly detected these Fe ii lines, as well as ad-ditional lines of Fe ii, Ca ii, Mg i, Mg ii, and O i. The restwavelengths of these lines are listed in Table 3, and theirprofiles are shown in Figure 3. We cannot inspect the time-resolved evolution of these lines as they are very weak andcorrespondingly noisy in the individual spectra.

It is evident that the four different species have distinctintensity distributions across the disc, which lead to the ob-served variety of line profile shapes. The sharp blue peak inthe Ca ii triplet is observed only in Mg i 8806 A and Ca ii8912, 8927 A. Rather surprisingly, the Ca H & K lines are

Table 3. Additional emission lines detected in the average X-

shooter spectrum (Figure 3) and the HST spectrum (Figure 4) ofSDSS J1228+1040). The rest wavelengths were obtained from theNIST Atomic Spectra Database.

Ion Rest wavelengths [A]

Ca ii 3933.66, 3968.47, 8498.02, 8542.09, 8662.14, 8912.078927.36

O i 7771.94, 7774.17, 7775.39, 8221.82, 8227.65, 8230.02,8233.00, 8235.35, 8446.36, 8446.76, 8820.43, 9260.81,9260.84, 9260.94, 9262.58, 9262.67, 9262.77, 9265.94,9266.01

Mg i 8806.76Mg ii 2795.53, 2798.00, 2802.70, 4481.13, 4481.33, 7877.05,

7896.37, 8234.64, 9218.25Fe ii 4923.92, 5018.44, 5169.03, 5197.57, 5234.62, 5276.00,

5316.61, 5316.78

different in shape to the Ca ii triplet, with a broad profile,much weaker in strength, and no clear asymmetry in theblue edge. They do, however, possibly show an extension tothe red similar to the Ca ii triplet, although the signal-to-noise ratio of the individual observations makes the pres-ence of such an extension uncertain. The O i lines at ≃ 7774and 8446 A show a clear red-dominated asymmetric profile,which has the opposite shape of the Ca ii triplet. The twoemission profiles at∼ 8245 (O i) and∼ 9250 A (O i and Mg ii)are blended, extending over a larger wavelength range witha blurred structure.

A number of emission profiles, such as Mg ii 7896 A,show sharp absorption features. These features are the pho-tospheric absorption lines, which is also the case at 5041and 5056 A, where a Si ii absorption doublet punctures thecontinuum.

We also show for reference theHST spectrum (Figure 4)obtained by Gansicke et al. (2012) in the far and near ul-traviolet spectral range. There are far more photosphericabsorption lines in the ultraviolet compared to the opticalrange, but only one emission line; Mg ii 2800 A, which wasfirst noted by Hartmann et al. (2011).

As done above for the Ca ii triplet, we measured themaximum red/blue velocities of the emission profiles in theoptical (where possible) to determine the radial extent of thedifferent species. The additional emission features are ordersof magnitude weaker than the strength of the Ca ii lines (seeTable 4), and it is therefore difficult to accurately determinethe maximum red and blue-shifted velocities. However, theprofiles have a similar FWZI in velocity space and as suchwe report the average velocities of the blue-most and red-most edge of the profiles as ≃ 400 kms−1 and ≃ 800 kms−1,respectively, which are consistent with those obtained for theCa ii triplet in all of the X-shooter observations so far. Thesimilarity in the maximum and minimum velocities suggeststhat the emitting ions share a similar location of their innerdisc edges. This is interesting to note as the line profiles differin shape, implying different intensity distributions across thedisc. Estimating an outer edge of the disc is much moredifficult, as most of the additional emission profiles only haveone clearly visible peak, and therefore a peak separationcannot be measured.

We compare the enlarged set of emission lines (Table 3)

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Figure 2. Time series of the continuum-divided Ca ii triplet in SDSS J1228+1040 in velocity space. The series runs over twelve yearswith 18 epochs and depicts the change in the morphology of the line profiles. The dashed and dot-dashed lines indicate the zero velocityposition, and the minimum and maximum velocities measured from the 2006 WHT data, respectively. The 2015 May profile is averagedfrom the X-shooter and UVES observations collected within several days of each other. The spectra are shifted in steps of three fromthe 2009 February (left) and 2015 May (right) observations.

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6 Christopher J. Manser et al.

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Figure 3. The averaged, continuum-divided X-shooter spectrum of SDSSJ 1228+1040 reveals additional emission lines with a wide rangeof morphologies and strengths. The bottom panel contains the Ca ii triplet, which extends far off of the plot, illustrating the extremelylarge dynamical range of the data. The ions that contribute to each profile are labelled in each panel, with dashed lines indicating theirrest wavelengths. The regions labelled as blends contain multiple lines (see Table 3).

to the predictions from Non-Local Thermodynamic Equilib-rium (NLTE) models of gaseous discs around white dwarfs(Hartmann et al. 2011). Each of the Ca and Mg lines de-tected in our X-shooter spectra are also present in the modelof Hartmann et al. (2011), although they also predict otherlines from these elements which we have not observed. Theselines may lie below the detection threshold of our data, e.g.the predicted Mg i 5173 A line is probably dominated by theemission of Fe ii 5169 A. We cannot compare our detectionsof Fe ii or O i as these are not included in the calculationsof Hartmann et al. (2011).

Hartmann et al. (2011) predict the Ca ii triplet to beflanked by emission of C ii 8700 A. By comparison withthe 2006 WHT spectra, the authors constrained the Cabundance in the disc to less than 0.46 per cent by mass.Gansicke et al. (2012) measured the C abundance of the de-bris accreted by SDSSJ1228+1040 from HST UV spectraand found a mass fraction of 0.02 per cent, consistent with

the non-detection of C emission in our deeper X-shooterspectra.

5 DOPPLER TOMOGRAPHY

While it is thought that the emission lines originate in agaseous disc with an assumed Keplerian velocity field, the in-tensity distribution across the disc is not known. The smoothmorphology variations of the Ca ii triplet imply a gradualchange in that distribution as viewed from Earth over thetwelve years of observations, which is astonishing when com-pared to the orbital period of the material in the disc, whichis of the order of a few hours.

One way of inducing the observed line profile vari-ation could be the rotation (precession) of a fixed non-axisymmetric intensity structure. This has been proposedto explain some of the features observed in the emission lineprofiles seen at Be stars. These stars are rapidly rotating and

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Figure 4. HST far (top) and near (bottom) ultraviolet observations of SDSS J1228+1040. The Mg ii emission line is labelled.

Table 4. Equivalent widths (EW) of the emission features shownin Figures 3& 4. The Ca ii triplet are set in bold.

Identifier Central wavelength [A] EW (error) [A]

Mg ii 2800 -7.9 (0.4)Ca ii 3934 -0.893 (0.007)Ca ii 3969 -1.485 (0.009)Mg ii 4481 -0.061 (0.002)Fe ii 4923 -0.243 (0.007)Fe ii 5018 -0.377 (0.008)Fe ii 5185 -1.60 (0.01)Fe ii 5235 -0.220 (0.009)Fe ii 5276 -0.478 (0.009)Fe ii 5317 -0.646 (0.007)O i 7774 -2.20 (0.02)Mg ii 7877 -0.78 (0.02)O i 8230 -0.71 (0.03)O i 8446 -1.50 (0.02)Ca ii 8498 -16.73 (0.03)Ca ii 8542 -23.45 (0.03)Ca ii 8662 -20.76 (0.03)Mg i, O i 8810 -1.73 (0.03)Ca ii 8920 -1.90 (0.03)O i, Mg ii 9234 -2.64 (0.05)

host circumstellar material in disc structures that frequentlyshow long term variability (Okazaki 1991; Papaloizou et al.1992; Okazaki 1997). Hanuschik et al. (1995) report line pro-files of Fe ii 5317 A (see their Figures 8, 14, and 15) seen inBe stars which are remarkably similar to the Ca ii tripletobservations of SDSSJ1228+1040.

To test the hypothesis of a fixed intensity structure, wefit the Ca ii triplet line profile using the method of Dopplertomography. Doppler tomography is commonly employed todeduce the structure of discs in accreting binary systems(Marsh & Horne 1988; Steeghs & Stehle 1999, see Marsh2001 for a review; in particular his Figure 3). Doppler tomog-

raphy produces a fixed intensity map (or Doppler map) invelocity space that, for a given period of rotation, best repli-cates the observed line profiles across all available epochs un-der the following assumptions (Marsh 2001): 1) All pointson the disc are equally visible at all times. 2) The flux fromany point fixed in the rotating frame is constant in time.3) All motion is parallel to the orbital plane. 4) The in-trinsic width of the profile from any point is negligible. TheDoppler map can also be used to reproduce an emission lineprofile for a given epoch by reducing the 2D intensity mapin velocity space to a 1D intensity distribution in the veloc-ity projected along the corresponding line of sight. Dopplermaps are useful tools to study disc structure as the conver-sion from coordinate space to velocity space is non-uniqueand multiple intensity profiles across a disc structure canproduce the same emission profile.

We used the 18 Ca ii triplet profiles collected forSDSSJ1228+1040 to produce Doppler maps with a range oftrial periods spanning 24.64 years (9000 days) to 68.45 years(25000 days) with increments of 500 days. We would not ex-pect a period much shorter than ≃ 25 years; otherwise thedisc would have precessed > 180◦, producing emission linesthat are the reflection of the 2003 March observation.

Doppler maps with periods between ∼ 24–30 years(∼ 9000–11000 days) appear very similar with only slightchanges in the shape of the intensity distribution. However,for periods longer than 30 years the maps of the disc becomeelongated or stretched, generating discontinuous changes invelocity not expected for Keplerian orbits. Maps with pe-riods longer than 30 years also generate emission profileswith an additional peak in each of the components of theCa ii triplet, which are not observed here or in other sys-tems with Ca ii emisison (see Section 7). We therefore adopta period in between 24–30 years; 27.4 years (10000 days) andthe Doppler map generated with this period is shown in Fig-ure 5. We also show a trailed spectrogram generated from theDoppler map over one full 27.4 years cycle (Figure 6). These

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8 Christopher J. Manser et al.

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Figure 5. An intensity distribution in velocity space of the Ca ii triplet, which models the line profiles observed in SDSS J1228+1040obtained from Doppler tomography. The white dwarf is located at the origin of the map where the lines intersect as a solid white circle.The solid white lines represent the epoch and line of sight for each observation from March 2003 to May 2015 and the dot-dashed whiteline indicates when we expect the Ca ii triplet to return to a morphology similar to that observed in 2003 (December 2016). The resultingprofile would be a reflection of the first observation, assuming a precession period of ≃ 27 years. The dashed white circles indicate thelocation of material in a Keplerian orbit around SDSS J1228+1040, with observed orbital radii (R sin2 i) of 0.2, 0.64, 1.2 and 2 R⊙, withthe largest circle (highest velocities) corresponding to 0.2R⊙, and the smallest circle (lowest velocities) to 2R⊙.

predictions will be compared against future spectroscopy ofthe Ca ii triplet in SDSSJ1228+1040.

The outer edge of the intensity structure corresponds tothe highest velocities and hence the inner edge of the disc incoordinate space. The inner edge is clearly asymmetric, witha large dispersed region and a narrow intense strip relatedto the large red-shifted velocities and the sharp blue-shiftedpeak seen in the emission profiles, respectively.

During the 2003–2008 observations, the dispersed andnarrow regions discussed above have projected velocitiesalong the line of sight which are significantly reduced, in-creasing the central strength near zero velocity rather thanthe extremes of the profile. The dashed lines in Figure 5 rep-

resent circular orbits in velocity space, underlining that theDoppler image of SDSSJ1228+1040 is highly non-circular,which agrees with our qualitative description of the line pro-files in Section 3. Further, this non-circularity cannot be de-scribed well as a single eccentricity, but rather by a changingeccentricity as a function of radius.

From the Doppler map we reconstructed the emissionfeatures observed in order to check for self consistency (Fig-ure 7). The line profiles generated from the Doppler map fitremarkably well for most epochs, although the sharpness ofthe red and blue-shifted peaks seen between 2008–2010 arenot totally replicated. The inability to fully reconstruct alldetails of the observed emission profiles may suggest that

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Doppler-imaging of a debris disc at a white dwarf 9

8520 8530 8540 8550 8560 8570

Wavelength [A]

2003 - 03

2008 - 09

2014 - 03

2019 - 08

2025 - 02

2030 - 08

Date

Figure 6. A trailed spectrogram generated from the Doppler mapin Figure 5 over one full 27.4 years cycle. The solid and dashedwhite tabs indicate the position in the spectrogram where wehave observed data, and the predicted halfway point respectively.

one or more of the assumptions underlying the method ofDoppler tomography are not fulfilled in SDSSJ1228+1040,e.g. there could be additional short term variability in thesystem.

An additional note regarding the interpretation of theDoppler map is that it depicts only the intensity distribu-tion of Ca ii. The difference in morphology between the Ca iitriplet and other ions, such as O i (see Section 3) suggeststhat these elements have different intensity distributionsacross the disc. Therefore Doppler maps of the emission linesof other ions in combination with that of Ca ii could revealadditional information on the physical conditions (e.g. den-sity, temperature) within the disc, if time-series spectroscopywith a sufficient signal-to-noise ratio is obtained.

6 A PRECESSING DISC?

We find that the data and the velocity map shown in Figure 5are largely consistent with a constant non-axisymmetric in-tensity structure that precesses around the white dwarf, re-sulting in a periodically varying projection into the observedemission line profiles. The precession and the structure of thedisc could be explained by several scenarios, which are notnecessarily mutually exclusive:

1) We are observing a young, eccentric disc that has onlyrecently formed from the tidal disruption of an asteroid. Ifonly gravitational forces are considered, the asteroid is dis-rupted and forms a broken, highly-eccentric ring of debrisaround the white dwarf, the majority of which is locatedoutside of the tidal disruption radius (Veras et al. 2014).Adding radiation forces causes the particles in the disc tospread inwards towards the white dwarf (on time-scales de-termined by their size), eventually circularising (Veras et al.2015). However, the time-scale on which a debris disc circu-larises is currently poorly known due to the complexity ofthe forces (e.g. radiation, gas drag) upon and the interac-tions (e.g. collisions) between the particles. If the circularisa-tion time-scale is significantly shorter than the twelve yearsspanned by our observations, we would expect the asym-metry in the emission features to have evolved towards aconstant, symmetric double-peaked line profile.

2) Precession due to general relativity. General relativis-tic effects will cause an eccentric orbit to precess over onefull orbit on a period Pω that is given by

Pω ≈ 84.98 yr

(

M

0.70M⊙

)−3/2(

a

1.00R⊙

)5/2(

1− e2)

(1)where M is the mass of the central star and a is the semi-major axis of the orbit (see Veras 2014 for details). In thelimit of small eccentricities we can ignore the term (1 −e2). By adopting Mwd = 0.7M⊙, we find precession periodsof 1.54, 27.8 and 134 years for orbits with semi-major axesof 0.2, 0.64R⊙ and 1.2 R⊙ respectively, i.e. the period ofprecession has a strong radial dependence.

General relativistic precession is intrinsic to any orbitalmechanics, and furthermore the period of 27.8 years for anorbit at 0.64R⊙ is close to the period range deduced fromour Doppler maps ≃ 24–30 years. Therefore it is expectedthat general relativity should have a significant contribu-tion to the variability observed in this system. The radialdependence of the precession period due to general relativ-ity will cause collisions among the dust particles on differentorbits, which is a possible mechanism for generating the ob-served gaseous component of the debris disc. These collisionswould also act to dampen the eccentricity into a circular or-bit, where production of gas due to general relativistic pre-cession would eventually cease. It is worth noting that theDoppler map (inherently) does not display the radial de-pendence of the general relativistic precession, which maybe dampened by other forces (e.g. gas pressure effects in thedisc).

3) An external perturber outside the disc inducing boththe eccentricity and precession. The flyby of a body orbitingon an eccentric orbit would perturb the orbits of the parti-cles in the disc. We have performed some numerical N-bodysimulations to determine the effect of an external perturber

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10 Christopher J. Manser et al.

8500 8600 8700

Wavelength [A]

0

5

10

15

20

25

Norm

alisedFlux

2003-03

2006-07

2007-04

2007-06

2007-07

2008-01

2008-06

2008-07

2009-02

8500 8600 8700

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0

5

10

15

20

25

Norm

alisedFlux

2009-04

2010-04

2011-04

2011-05

2011-06

2012-03

2014-03

2014-06

2015-05

Figure 7. The continuum-divided Ca ii triplet line profiles (black) for SDSS J1228+1040 in chronological order (as in Figure 2) recon-structed (red) using the Doppler map in Figure 5 with residuals (grey). The spectra are shifted in steps of three from the 2009 February(left) and 2015 May observations (right).

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Doppler-imaging of a debris disc at a white dwarf 11

on circular rings of particles located at about one Solar ra-dius from the white dwarf. Because the asymptotic giantbranch progenitor of SDSSJ1228+1040 had a radius of atleast 2.5–3.0 au, surviving planet-sized perturbers must nowhave a semimajor axis exceeding 3–11 au (see, e.g. Figure10 of Mustill & Villaver 2012). Consequently, a perturber’scurrent orbital period must be at least several years, whichcovers multiple observations from Figure 7, in particular dur-ing the years 2007–2008, where the observations are closelyspaced. We therefore adopted a perturber semimajor axis of5 au, with masses (100 − 104M⊕) and eccentricities (0.990–0.998 - a realistic possibility; see Debes & Sigurdsson 2002;Veras et al. 2013; Voyatzis et al. 2013; Mustill et al. 2014;Bonsor & Veras 2015; Veras & Gansicke 2015) in rangesthat might produce an observable eccentricity change in thering. Smaller mass perturbers would have to approach soclose to the ring particles to potentially be in danger oftidally disrupting.

Each simulation contained 210 massless ring par-ticles, and spanned one close encounter. The whitedwarf mass was set at 0.705M⊙, and the particleswere equally partitioned into seven rings at distances of{0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2R⊙}. We uniformly distributedthe initial mean anomalies of the particles within each ring.

In every case changes in ring particle eccentricity oc-curred only within a few hours of a close encouter. Duringthe remainder of the orbit, there was no eccentricity change.Therefore, in-between encounters (spanning several years),the geometry of the disc did not change, which is at oddswith the observations from Figure 7. This mismatch wouldalso hold true for perturbers with initially greater semimajoraxes.

4) The disc induces its own eccentricity and precession.Statler (2001) has shown that an eccentric flat fluid disc canprecess due to the pressure gradient generated within thedisc. Figure 3 from Statler (2001) shows line profiles thatare similar in morphology to that of SDSSJ1228+1040 (seeSection 3). In contrast to these simulations of purely fluiddiscs, the gaseous discs that we have observed are coupledto dust grains. Kinnear (2011) finds a typical gas mass, Mgas,of ∼ 1019 g. Estimates of the dust mass, Mdust, range from1019 to 1024 g, from disc models that reproduce the observedinfrared excess in systems with dusty discs (see, Jura et al.2007; Jura 2008; Reach et al. 2009), i.e. Mgas 6 Mdust andas such we can not assume the disc is dominated by thegaseous component. Finally, it is worth noting that Ogilvie(2001) finds that the eccentricity in a disc will dissipate onthe viscous time-scale, which we estimate to be ≃ 5-20 years(Section 6), i.e. similar to our observational baseline. Giventhat the eccentricity in SDSSJ1228+1040 persists over thistime scale, self-induction seems unlikely.

Of the different scenarios outlined above, a young ec-centric disc that precesses due to general relativity appearsto be the most natural scenario that can describe our obser-vations. We would also expect this phase to be fairly short-lived, which would explain the rarity of detected gaseousdebris disc components. Assuming the adopted precessionperiod of 27.4 years, the system is expected to reach halfway through the precession cycle in December 2016, i.e. wewould expect a Ca ii triplet morphology that is the reflec-tion of the March 2003 observations. In the next section wediscuss the variability seen in other gaseous discs around

white dwarfs and the possible generation mechanisms forthese systems.

7 DISCUSSION

Besides the observations of SDSS J1228+1040 presentedhere, changes in the Ca ii emission lines have beenreported for two other systems with a gaseous disc;SDSSJ0845+2258, and SDSSJ1617+1620 (Wilson et al.2014, 2015). In SDSSJ0845+2257 the Ca ii profiles evolvedin shape from a strong, red-dominated asymmetry to aslight, blue-dominated symmetric profile over a time-scaleof ten years; similar to the overall variation seen in theCa ii triplet of SDSSJ1228+1040. In contrast, morpho-logical changes in the line profile were not apparent inSDSSJ1617+1620, where the Ca ii emission lines from thegaseous disc remained symmetric (suggesting an axisymmet-ric intensity pattern) and decreased in strength, eventuallydisappearing within eight years (Wilson et al. 2014).

There are four other white dwarfs known to hosta gaseous disc: SDSSJ104341.53+085558.2 (hence-forth SDSSJ1043+0855), SDSSJ073842.56+183509.6(henceforth SDSSJ0738+1835), SDSSJ0959–0200,and HE1349–2305. Of these four systems onlySDSSJ1043+0855 and SDSSJ0738+1835 have multi-epoch spectroscopy. SDSSJ1043+0855 shows variabilitysimilar to SDSSJ1228+1040 although only a handful ofepochs are available so far (Manser et al. 2016). In contrast,SDSSJ0738+1835 shows no change in the shape or strengthof the Ca ii triplet over a period of six years (Gansicke2011; Dufour et al. 2012). However, with only threeepochs, more data is needed to confirm the steady stateof SDSSJ0738+1835. The emission lines in HE1349–2305show a large asymmetry similar to the systems with a mor-phological variation (SDSSJ1228+1040, SDSSJ1043+0855and SDSSJ0845+2257), and therefore this star would bean ideal candidate for follow up observations to detectvariability (Melis et al. 2012). The Ca ii triplet observed atSDSSJ0959–0200 is much narrower and weaker than thatof the other six systems, indicating a low inclination of thedisc with respect to the line of sight (Farihi et al. 2012).Finally, Guo et al. (2015) recently identified the candidategas disc at SDSSJ114404.74+052951.6 which has Ca iiemission similar that of SDSSJ0959–0200. The system alsoshows infrared excess attributed to a dusty debris disc,but the Ca ii emission lines are extremely weak, and followup observations are needed to confirm the presence of agaseous component.

The gaseous component of a debris disc will accrete ontothe white dwarf, and without a sustained generation mech-anism will dissipate over the viscous time-scale, which canbe estimated using equation 2 from Metzger et al. (2012).The major uncertainty is the value of α, the accretion discviscosity parameter (Shakura & Sunyaev 1973). King et al.(2007) suggest 0.1 6 α 6 0.4 for a thin fully ionised disc.Given that the metallic gas is ionised to a high degree, itis plausible to adopt this range for α, which leads to vis-cous time-scales of 5–20 years for a typical white dwarf mass.These time-scales match the disappearance of the Ca ii linesobserved in SDSSJ1617+1620 discussed above.

We calculated the equivalent width of the Ca ii triplet

MNRAS 000, 1–13 (20XX)

12 Christopher J. Manser et al.

Table 5. Equivalent width measurements of the Ca ii triplet in

SDSS J1228+1040.

Date Equivalent width [A]

2003–03 -60 (7)2006–07 -69 (2)2007–04 -61 (2)2007–06 -63 (2)2007–07 -63 (2)2008–01 -60 (2)2008–06 -54 (2)2008–07 -60 (2)2009–02 -58 (2)2009–04 -62 (2)2010–04 -67 (1)2011–01 -57 (1)2011–05 -60 (1)2011–06 -59 (1)2012–03 -56 (1)2014–03 -50 (1)2014–06 -52 (1)2015–05 -57 (1)

for SDSSJ1228+1040 for each epoch (Table 5), and donot detect any significant decrease, suggesting that; 1) thegaseous discs in SDSSJ1228+1040 and SDSSJ0845+2257are being sustained by ongoing gas production, and 2) theremay be multiple pathways to generate a gaseous disc giventhat there are clear differences in the type of variability seenin these three systems and SDSSJ1617+1620.

From Section 6, a natural scenario to explain the mor-phology variation is that of a young eccentric disc that pre-cesses due to general relativity with the radial dependenceof the precession period resulting in ongoing collisional gasproduction that ceases once the disc circularises. This sce-nario allows for gas generation, while not being mutuallyexclusive with the observations of SDSSJ1617+1620, whichwould be better explained by a transient event such as asecondary asteroid impact onto a pre-existing, circulariseddisc (Jura 2008). Such an asteroid impact would generatean initial quantity of gas that would subsequently dissipateover the viscous time-scale.

The relatively short-lived transient nature of thesegas generation mechanisms also explains why thereare systems with accretion rates much larger thanthat of SDSSJ1228+1040, such as PG 0843+516 andGALEX1931+0117, which do not show any sign of a gaseousdisc (Gansicke et al. 2012). We expect that debris discs withno detectable gaseous component are largely circularised.

8 CONCLUSIONS

We report the pronounced morphology changes of the Ca iitriplet at SDSSJ1228+1040 which we have modelled usingthe method of Doppler tomography. This procedure pro-duced a non-axisymmetric intensity map in velocity spaceof the Ca ii triplet, which we have interpreted as a precess-ing disc with a period in the range 24–30 years. We alsodetected additional emission lines in the averaged X-shooterspectra of SDSSJ1228+1040, increasing the number of ob-served gaseous elements in this system to four. The variation

in shape between the emission features of different ions is aclear indication that the intensity distribution in the disc foreach ion is not the same. With time-resolved spectroscopyand sufficient signal-to-noise, Doppler tomography of the ad-ditional line profiles (such as O i 7774, 8446 A) may revealinformation about the physical properties in the disc (e.gdensity and temperature distributions).

The gaseous component of debris discs are a tracer ofdynamical activity in these systems. Four of the five gaseousdiscs with time-resolved observations over time-scales ofyears show variability, and small-number statistics so farsuggest that the dynamic variability of the gaseous discsthemselves is the the norm rather than the exception.

ACKNOWLEDGEMENTS

We thank the referee for their helpful comments and sug-gestions for improving this manuscript. The research lead-ing to these results has received funding from the Euro-pean Research Council under the European Union’s Sev-enth Framework Programme (FP/2007-2013) / ERC GrantAgreement n. 320964 (WDTracer). We would like to thankYan-Ping Chen and Scott Trager for sharing their X-shootertelluric template library. TRM acknowledges support fromthe Science and Technology Facilities Council (STFC), grantST/L000733/1. SGP acknowledges financial support fromFONDECYT in the form of grant number 3140585. CJMwould like to thank Mark Hollands for his help with Fig-ure 1.

Based on observations made with ESO Telescopes atthe La Silla Paranal Observatory under programme IDs:079.C-0085, 081.C-0466, 082.C-0495, 087.D-0139, 088.D-0042, 093.D-0426, 095.D-0802, 192.D-0270, 383.C-0695,386.C-0218, 595.C-0650. This work has made use of obser-vations from the SDSS-III, funding for which has been pro-vided by the Alfred P. Sloan Foundation, the ParticipatingInstitutions, the National Science Foundation, and the U.S.Department of Energy Office of Science. The SDSS-III website is http://www.sdss3.org/. Based on observations madewith the NASA/ESA HST, obtained at the Space TelescopeScience Institute, which is operated by the Association ofUniversities for Research in Astronomy, Inc., under NASAcontract NAS 5-26555. These observations are associatedwith program 11561. Based on observations made with theWHT operated on the island of La Palma by the Isaac New-ton Group in the Spanish Observatorio del Roque de losMuchachos of the Instituto de Astrofsica de Canarias.

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